102 citations · 287 across the 18 of their papers we have counts for
10 papers · 1 filter
Time-reversibility and integrability of p:-q resonant vector fields
Jaume Gine, Valery G. Romanovski, Joan Torregrosa
We study local analytical integrability in a neighborhood of resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect…
Analytic integrability around a nilpotent singularity
Antonio Algaba, Cristobal Garcia, Jaume Gine
In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.
Essential perturbations of polynomial vector fields with a period annulus
Adriana Buică, Jaume Giné, Maite Grau
In this paper we first give the explicit definition of essential perturbation. Secondly, given a perturbation of a particular family of centers of polynomial differential systems o…
Weierstrass integrability of differential equations
Jaume Giné, Maite Grau
The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterizatio…
Linearizable ordinary differential equations
Hector Giacomini, Jaume Gine, Maite Grau
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be co…
On the cyclicity of weight-homogeneous centers
Lubomir Gavrilov, Jaume Gine, Maite Grau
Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W…
A note on "Relaxation Oscillators with Exact Limit Cycles"
Jaume Giné, Maite Grau
In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an exampl…
The role of algebraic solutions in planar polynomial differential systems
Héctor Giacomini, Jaume Giné, Maite Grau
We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=…
Integrability of planar polynomial differential systems through linear differential equations
Héctor Giacomini, Jaume Giné, Maite Grau
In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients. We give a method to con…
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
Héctor Giacomini, Jaume Giné, Jaume Llibre
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type cent…